*-*-*-*-*-*-*-*-*Smooth data with Kernel smoother*-*-*-*-*-*-*-*-*-*-*
================================
Smooth grin with the Nadaraya-Watson kernel regression estimate.
Arguments:
grin: input graph
option: the kernel to be used: "box", "normal"
bandwidth: the bandwidth. The kernels are scaled so that their quartiles
(viewed as probability densities) are at +/- 0.25*bandwidth.
nout: If xout is not specified, interpolation takes place at equally
spaced points spanning the interval [min(x), max(x)], where
nout = max(nout, number of input data).
xout: an optional set of values at which to evaluate the fit

*-*-*-*-*-*-*-*-*Smooth data with Lowess smoother*-*-*-*-*-*-*-*-*-*-*
================================
This function performs the computations for the LOWESS smoother
(see the reference below). Lowess returns the output points
x and y which give the coordinates of the smooth.
Arguments:
grin: Input graph
span: the smoother span. This gives the proportion of points in the plot
which influence the smooth at each value.
Larger values give more smoothness.
iter: the number of robustifying iterations which should be performed.
Using smaller values of iter will make lowess run faster.
delta: values of x which lie within delta of each other replaced by a
single value in the output from lowess.
For delta = 0, delta will be calculated.
References:
Cleveland, W. S. (1979) Robust locally weighted regression and smoothing
scatterplots. J. Amer. Statist. Assoc. 74, 829-836.
Cleveland, W. S. (1981) LOWESS: A program for smoothing scatterplots
by robust locally weighted regression.
The American Statistician, 35, 54.
==================

*-*-*-*-*-*-*-*-*Smooth data with Super smoother*-*-*-*-*-*-*-*-*-*-*-*
===============================
Smooth the (x, y) values by Friedman's ``super smoother''.
Arguments:
grin: graph for smoothing
span: the fraction of the observations in the span of the running lines
smoother, or 0 to choose this by leave-one-out cross-validation.
bass: controls the smoothness of the fitted curve.
Values of up to 10 indicate increasing smoothness.
isPeriodic: if TRUE, the x values are assumed to be in [0, 1]
and of period 1.
w: case weights
Details:
supsmu is a running lines smoother which chooses between three spans for
the lines. The running lines smoothers are symmetric, with k/2 data points
each side of the predicted point, and values of k as 0.5 * n, 0.2 * n and
0.05 * n, where n is the number of data points. If span is specified,
a single smoother with span span * n is used.
The best of the three smoothers is chosen by cross-validation for each
prediction. The best spans are then smoothed by a running lines smoother
and the final prediction chosen by linear interpolation.
The FORTRAN code says: ``For small samples (n < 40) or if there are
substantial serial correlations between observations close in x - value,
then a prespecified fixed span smoother (span > 0) should be used.
Reasonable span values are 0.2 to 0.4.''
References:
Friedman, J. H. (1984) SMART User's Guide.
Laboratory for Computational Statistics,
Stanford University Technical Report No. 1.
Friedman, J. H. (1984) A variable span scatterplot smoother.
Laboratory for Computational Statistics,
Stanford University Technical Report No. 5.
==================

*-*-*-*-*-*-*-*-*Approximate data points*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*
=======================
Arguments:
grin: graph giving the coordinates of the points to be interpolated.
Alternatively a single plotting structure can be specified:
option: specifies the interpolation method to be used.
Choices are "linear" (iKind = 1) or "constant" (iKind = 2).
nout: If xout is not specified, interpolation takes place at n equally
spaced points spanning the interval [min(x), max(x)], where
nout = max(nout, number of input data).
xout: an optional set of values specifying where interpolation is to
take place.
yleft: the value to be returned when input x values less than min(x).
The default is defined by the value of rule given below.
yright: the value to be returned when input x values greater than max(x).
The default is defined by the value of rule given below.
rule: an integer describing how interpolation is to take place outside
the interval [min(x), max(x)]. If rule is 0 then the given yleft
and yright values are returned, if it is 1 then 0 is returned
for such points and if it is 2, the value at the closest data
extreme is used.
f: For method="constant" a number between 0 and 1 inclusive,
indicating a compromise between left- and right-continuous step
functions. If y0 and y1 are the values to the left and right of
the point then the value is y0*f+y1*(1-f) so that f=0 is
right-continuous and f=1 is left-continuous
ties: Handling of tied x values. An integer describing a function with
a single vector argument returning a single number result:
ties = "ordered" (iTies = 0): input x are "ordered"
ties = "mean" (iTies = 1): function "mean"
ties = "min" (iTies = 2): function "min"
ties = "max" (iTies = 3): function "max"
Details:
At least two complete (x, y) pairs are required.
If there are duplicated (tied) x values and ties is a function it is
applied to the y values for each distinct x value. Useful functions in
this context include mean, min, and max.
If ties="ordered" the x values are assumed to be already ordered. The
first y value will be used for interpolation to the left and the last
one for interpolation to the right.
Value:
approx returns a graph with components x and y, containing n coordinates
which interpolate the given data points according to the method (and rule)
desired.

This page has been automatically generated. If you have any comments or suggestions about the page layout send a mail to ROOT support, or contact the developers with any questions or problems regarding ROOT.